"... this paper is to propose a finite difference sheme for the FokkerPlanck equation (1.1)--(1.3) which preserves the conservation laws of mass, momentum and energy. Previous finite difference conservative schemes have been proposed in [3] for the isotropic case and in [12--14] for the azimuthal symmetr ..."

this paper is to propose a finite difference sheme for the FokkerPlanck equation (1.1)--(1.3) which preserves the conservation laws of mass, momentum and energy. Previous finite difference conservative schemes have been proposed in [3] for the isotropic case and in [12--14] for the azimuthal

"... A new formulation for collisional kinetic theory is presented based on the use of Lietransform methods to eliminate fast orbital time scales from a general bilinear collision operator. As an application of this new formalism, a general guiding-center bilinear Fokker-Planck (FP) collision operator is ..."

A new formulation for collisional kinetic theory is presented based on the use of Lietransform methods to eliminate fast orbital time scales from a general bilinear collisionoperator. As an application of this new formalism, a general guiding-center bilinear Fokker-Planck (FP) collisionoperator

"... Numerical energy conservation in Fokker–Planck problems requires the energy moment of the Fokker–Planck equation to cancel exactly. However, standard dis-cretization techniques not only do not observe this requirement (thus precluding exact energy conservation), but they also demand very refined mes ..."

collisionoperator using Maxwell stress tensor formalism. As a result, the Fokker–Planckcollisionoperator takes the form of a double diver-gence operating on a tensor, which is suitable for particle and energy conservative differencing. Numerical results show that the new discretization scheme improves

"... We derive the Fokker-Planck operator describing a highly forward peaked scattering process in the linear transport equation, in anisotropic media, as a formal asymptotic limit of the exact integral operator. The resulting operator, being both convective and diffusive in angle and energy variables ..."

We derive the Fokker-Planckoperator describing a highly forward peaked scattering process in the linear transport equation, in anisotropic media, as a formal asymptotic limit of the exact integral operator. The resulting operator, being both convective and diffusive in angle and energy

"... The Fokker--Planck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of time--dependent systems in which randomness plays a role. In this paper, ..."

The Fokker--Planck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of time--dependent systems in which randomness plays a role. In this paper

"... We give a sequence of operators approximating the Fokker-PlanckLandau collision operator. This sequence is obtained by aplying the fast multipole method based on the work by Greengard and Rocklin [17], and tends to the exact Fokker-Planck-Landau operator with an arbitrary accuracy. These operators s ..."

We give a sequence of operators approximating the Fokker-PlanckLandau collisionoperator. This sequence is obtained by aplying the fast multipole method based on the work by Greengard and Rocklin [17], and tends to the exact Fokker-Planck-Landau operator with an arbitrary accuracy. These operators

"... The chemical master equation (CME) describes the probability for the discrete molecular copy numbers that define the state of a chemical system. Each molecular species in the chemical model adds a dimension to the state space. The CME is a difference-differential equation which can be solved numeric ..."

numerically if the state space is truncated at an upper limit of the copy number in each dimension. The size of the truncated CME suffers from an exponential growth for an increasing number of chemical species. In this thesis the CME is approximated by a continuous Fokker-Planck equation (FPE) which makes